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                <h2 id="1-冒泡排序"><a href="#1-冒泡排序" class="headerlink" title="1.冒泡排序"></a>1.冒泡排序</h2><pre class=" language-java"><code class="language-java"><span class="token keyword">public</span> <span class="token keyword">static</span> <span class="token keyword">void</span> <span class="token function">bubblesort</span><span class="token punctuation">(</span><span class="token keyword">int</span><span class="token punctuation">[</span><span class="token punctuation">]</span> arr<span class="token punctuation">)</span><span class="token punctuation">{</span>

    <span class="token comment" spellcheck="true">//冒泡排序的时间复杂度o(n*2)</span>
    <span class="token comment" spellcheck="true">//标识符</span>
    <span class="token keyword">boolean</span> flag <span class="token operator">=</span> <span class="token boolean">false</span><span class="token punctuation">;</span>
    <span class="token keyword">for</span><span class="token punctuation">(</span><span class="token keyword">int</span> i <span class="token operator">=</span><span class="token number">0</span> <span class="token punctuation">;</span>i<span class="token operator">&lt;</span>arr<span class="token punctuation">.</span>length<span class="token operator">-</span><span class="token number">1</span><span class="token punctuation">;</span>i<span class="token operator">++</span><span class="token punctuation">)</span><span class="token punctuation">{</span>
        <span class="token keyword">for</span> <span class="token punctuation">(</span><span class="token keyword">int</span> j <span class="token operator">=</span> <span class="token number">0</span><span class="token punctuation">;</span> j <span class="token operator">&lt;</span> arr<span class="token punctuation">.</span>length <span class="token operator">-</span> <span class="token number">1</span><span class="token operator">-</span>i<span class="token punctuation">;</span> j<span class="token operator">++</span><span class="token punctuation">)</span> <span class="token punctuation">{</span>
            <span class="token comment" spellcheck="true">//如果前面的数比后面的数大，则交换</span>
            <span class="token keyword">if</span> <span class="token punctuation">(</span>arr<span class="token punctuation">[</span>j<span class="token punctuation">]</span> <span class="token operator">></span> arr<span class="token punctuation">[</span>j <span class="token operator">+</span> <span class="token number">1</span><span class="token punctuation">]</span><span class="token punctuation">)</span> <span class="token punctuation">{</span>
                flag <span class="token operator">=</span> <span class="token boolean">true</span><span class="token punctuation">;</span>
                <span class="token keyword">int</span> temp <span class="token operator">=</span> arr<span class="token punctuation">[</span>j<span class="token punctuation">]</span><span class="token punctuation">;</span>
                arr<span class="token punctuation">[</span>j<span class="token punctuation">]</span> <span class="token operator">=</span> arr<span class="token punctuation">[</span>j <span class="token operator">+</span> <span class="token number">1</span><span class="token punctuation">]</span><span class="token punctuation">;</span>
                arr<span class="token punctuation">[</span>j <span class="token operator">+</span> <span class="token number">1</span><span class="token punctuation">]</span> <span class="token operator">=</span> temp<span class="token punctuation">;</span>
            <span class="token punctuation">}</span>
        <span class="token punctuation">}</span>

        <span class="token comment" spellcheck="true">//在一次排序中,一次都没交换过</span>
        <span class="token keyword">if</span><span class="token punctuation">(</span><span class="token operator">!</span>flag<span class="token punctuation">)</span><span class="token punctuation">{</span>
            <span class="token keyword">break</span><span class="token punctuation">;</span>
        <span class="token punctuation">}</span><span class="token keyword">else</span> <span class="token punctuation">{</span>
            <span class="token comment" spellcheck="true">//重置flag，下次判断</span>
            flag <span class="token operator">=</span> <span class="token boolean">false</span><span class="token punctuation">;</span>
        <span class="token punctuation">}</span>
    <span class="token punctuation">}</span>
<span class="token punctuation">}</span>
</code></pre>
<h2 id="2-选择排序"><a href="#2-选择排序" class="headerlink" title="2.选择排序"></a>2.选择排序</h2><p><img src="https://img-blog.csdnimg.cn/img_convert/76339a259488423b03370e381ca5edb0.gif" alt="选择排序"></p>
<pre class=" language-java"><code class="language-java"><span class="token keyword">public</span> <span class="token keyword">static</span> <span class="token keyword">void</span> <span class="token function">selectSort</span><span class="token punctuation">(</span><span class="token keyword">int</span><span class="token punctuation">[</span><span class="token punctuation">]</span> arr<span class="token punctuation">)</span> <span class="token punctuation">{</span>


        <span class="token keyword">for</span> <span class="token punctuation">(</span><span class="token keyword">int</span> i <span class="token operator">=</span> <span class="token number">0</span><span class="token punctuation">;</span> i <span class="token operator">&lt;</span> arr<span class="token punctuation">.</span>length <span class="token operator">-</span> <span class="token number">1</span><span class="token punctuation">;</span> i<span class="token operator">++</span><span class="token punctuation">)</span> <span class="token punctuation">{</span>
            <span class="token keyword">int</span> minIndex <span class="token operator">=</span> i<span class="token punctuation">;</span>
            <span class="token keyword">int</span> min <span class="token operator">=</span> arr<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token punctuation">;</span>
            <span class="token comment" spellcheck="true">//第一轮</span>
            <span class="token keyword">for</span> <span class="token punctuation">(</span><span class="token keyword">int</span> j <span class="token operator">=</span> i <span class="token operator">+</span> <span class="token number">1</span><span class="token punctuation">;</span> j <span class="token operator">&lt;</span> arr<span class="token punctuation">.</span>length<span class="token punctuation">;</span> j<span class="token operator">++</span><span class="token punctuation">)</span> <span class="token punctuation">{</span>
                <span class="token comment" spellcheck="true">//说明定的最小值不是最小的</span>
                <span class="token keyword">if</span> <span class="token punctuation">(</span>min <span class="token operator">></span> arr<span class="token punctuation">[</span>j<span class="token punctuation">]</span><span class="token punctuation">)</span> <span class="token punctuation">{</span>
                    <span class="token comment" spellcheck="true">//重置最小值</span>
                    min <span class="token operator">=</span> arr<span class="token punctuation">[</span>j<span class="token punctuation">]</span><span class="token punctuation">;</span>
                    minIndex <span class="token operator">=</span> j<span class="token punctuation">;</span>
                <span class="token punctuation">}</span>
            <span class="token punctuation">}</span>

            <span class="token comment" spellcheck="true">//将最小值与arr[0]交换</span>
            <span class="token keyword">if</span><span class="token punctuation">(</span>minIndex <span class="token operator">!=</span>  i<span class="token punctuation">)</span><span class="token punctuation">{</span>
                arr<span class="token punctuation">[</span>minIndex<span class="token punctuation">]</span> <span class="token operator">=</span> arr<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token punctuation">;</span>
                arr<span class="token punctuation">[</span>i<span class="token punctuation">]</span> <span class="token operator">=</span> min<span class="token punctuation">;</span>
            <span class="token punctuation">}</span>
        <span class="token punctuation">}</span>
<span class="token punctuation">}</span>
</code></pre>
<h2 id="3-插入排序"><a href="#3-插入排序" class="headerlink" title="3.插入排序"></a>3.插入排序</h2><p><img src="https://img-blog.csdnimg.cn/img_convert/c894e22dcc48b03559e3087627e3dbb8.gif" alt="插入排序"></p>
<pre class=" language-java"><code class="language-java"> <span class="token keyword">public</span> <span class="token keyword">static</span> <span class="token keyword">void</span> <span class="token function">insertSort</span><span class="token punctuation">(</span><span class="token keyword">int</span><span class="token punctuation">[</span><span class="token punctuation">]</span> arr<span class="token punctuation">)</span><span class="token punctuation">{</span>
        <span class="token comment" spellcheck="true">//使用逐步推导的方式</span>

        <span class="token keyword">int</span> insertVal <span class="token operator">=</span> <span class="token number">0</span><span class="token punctuation">;</span>
        <span class="token keyword">int</span> insertIndex <span class="token operator">=</span> <span class="token number">0</span><span class="token punctuation">;</span>

        <span class="token keyword">for</span><span class="token punctuation">(</span><span class="token keyword">int</span> i <span class="token operator">=</span> <span class="token number">1</span><span class="token punctuation">;</span> i<span class="token operator">&lt;</span>arr<span class="token punctuation">.</span>length<span class="token punctuation">;</span>i<span class="token operator">++</span><span class="token punctuation">)</span> <span class="token punctuation">{</span>
            <span class="token comment" spellcheck="true">//定义待插入的数</span>
             insertVal <span class="token operator">=</span> arr<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token punctuation">;</span>
            <span class="token comment" spellcheck="true">//即arr[1]前面这个数的下标</span>
             insertIndex <span class="token operator">=</span> i <span class="token operator">-</span> <span class="token number">1</span><span class="token punctuation">;</span>
            <span class="token comment" spellcheck="true">//说明</span>
            <span class="token comment" spellcheck="true">//insertIndex >= 0保证在给insertVal找插入位置，不越界</span>
            <span class="token comment" spellcheck="true">//insertVal &lt; arr[insertIndex] 待插入的数， 还没有找到插入位置</span>
            <span class="token comment" spellcheck="true">//给insertVal找到插入位置</span>
            <span class="token keyword">while</span> <span class="token punctuation">(</span>insertIndex <span class="token operator">>=</span> <span class="token number">0</span> <span class="token operator">&amp;&amp;</span> insertVal <span class="token operator">&lt;</span> arr<span class="token punctuation">[</span>insertIndex<span class="token punctuation">]</span><span class="token punctuation">)</span> <span class="token punctuation">{</span>

                <span class="token comment" spellcheck="true">//就需要将arr[insertIndex]后移</span>
                arr<span class="token punctuation">[</span>insertIndex <span class="token operator">+</span> <span class="token number">1</span><span class="token punctuation">]</span> <span class="token operator">=</span> arr<span class="token punctuation">[</span>insertIndex<span class="token punctuation">]</span><span class="token punctuation">;</span>

                insertIndex<span class="token operator">--</span><span class="token punctuation">;</span>

            <span class="token punctuation">}</span>
            <span class="token comment" spellcheck="true">//当退出这个循环时，说明插入的位置找到</span>
            <span class="token keyword">if</span><span class="token punctuation">(</span>insertIndex <span class="token operator">+</span> <span class="token number">1</span> <span class="token operator">!=</span> i<span class="token punctuation">)</span><span class="token punctuation">{</span>
                arr<span class="token punctuation">[</span>insertIndex <span class="token operator">+</span> <span class="token number">1</span><span class="token punctuation">]</span> <span class="token operator">=</span> insertVal<span class="token punctuation">;</span>
            <span class="token punctuation">}</span>
        <span class="token punctuation">}</span>
 <span class="token punctuation">}</span>
</code></pre>
<h2 id="4-希尔排序"><a href="#4-希尔排序" class="headerlink" title="4.希尔排序"></a>4.希尔排序</h2><p><img src="https://img-blog.csdnimg.cn/07b15ca5a0cd4d52bfe66fe0f5dba8a2.gif#pic_center" alt="在这里插入图片描述"></p>
<p>希尔排序的时间复杂度是：O（nlogn）～O（n2），平均时间复杂度大致是O(n√n)</p>
<p>笔者的理解是时间复杂度取决于你所选用的gap。因为希尔排序事先将无序的数组处理了一下，使其变得部分有序</p>
<p>最后再在gap &#x3D; 1的情况下进行插入排序，所以，我认为希尔排序是一个加强的插入排序</p>
<pre class=" language-java"><code class="language-java"><span class="token keyword">public</span> <span class="token keyword">static</span> <span class="token keyword">void</span> <span class="token function">shellSort2</span><span class="token punctuation">(</span><span class="token keyword">int</span><span class="token punctuation">[</span><span class="token punctuation">]</span> arr<span class="token punctuation">)</span> <span class="token punctuation">{</span>

    <span class="token keyword">for</span> <span class="token punctuation">(</span><span class="token keyword">int</span> gap <span class="token operator">=</span> arr<span class="token punctuation">.</span>length <span class="token operator">/</span> <span class="token number">2</span><span class="token punctuation">;</span> gap <span class="token operator">></span> <span class="token number">0</span><span class="token punctuation">;</span> gap <span class="token operator">/=</span> <span class="token number">2</span><span class="token punctuation">)</span> <span class="token punctuation">{</span>
         <span class="token comment" spellcheck="true">//对数组进行分组</span>
        <span class="token keyword">for</span> <span class="token punctuation">(</span><span class="token keyword">int</span> i <span class="token operator">=</span> gap<span class="token punctuation">;</span> i <span class="token operator">&lt;</span> arr<span class="token punctuation">.</span>length<span class="token punctuation">;</span> i<span class="token operator">++</span><span class="token punctuation">)</span> <span class="token punctuation">{</span>
            <span class="token keyword">int</span> j <span class="token operator">=</span> i<span class="token punctuation">;</span>
            <span class="token keyword">int</span> temp <span class="token operator">=</span> arr<span class="token punctuation">[</span>j<span class="token punctuation">]</span><span class="token punctuation">;</span>
            <span class="token comment" spellcheck="true">//变相的插入排序，不过其中的间隔不再是1，而是gap</span>
            <span class="token keyword">if</span> <span class="token punctuation">(</span>arr<span class="token punctuation">[</span>j<span class="token punctuation">]</span> <span class="token operator">&lt;</span> arr<span class="token punctuation">[</span>j <span class="token operator">-</span> gap<span class="token punctuation">]</span><span class="token punctuation">)</span> <span class="token punctuation">{</span>  <span class="token comment" spellcheck="true">// 优化，如果不存在arr[j - gap] > arr[j],则不执行</span>
                <span class="token keyword">while</span> <span class="token punctuation">(</span>j <span class="token operator">-</span> gap <span class="token operator">>=</span> <span class="token number">0</span> <span class="token operator">&amp;&amp;</span> temp <span class="token operator">&lt;</span> arr<span class="token punctuation">[</span>j <span class="token operator">-</span> gap<span class="token punctuation">]</span><span class="token punctuation">)</span> <span class="token punctuation">{</span>

                    arr<span class="token punctuation">[</span>j<span class="token punctuation">]</span> <span class="token operator">=</span> arr<span class="token punctuation">[</span>j <span class="token operator">-</span> gap<span class="token punctuation">]</span><span class="token punctuation">;</span>
                    j <span class="token operator">-=</span> gap<span class="token punctuation">;</span>

                <span class="token punctuation">}</span>
                arr<span class="token punctuation">[</span>j<span class="token punctuation">]</span> <span class="token operator">=</span> temp<span class="token punctuation">;</span>
            <span class="token punctuation">}</span>

        <span class="token punctuation">}</span>
    <span class="token punctuation">}</span>
<span class="token punctuation">}</span>
</code></pre>
<h2 id="5-快速排序"><a href="#5-快速排序" class="headerlink" title="5.快速排序"></a>5.快速排序</h2><p><img src="https://img-blog.csdnimg.cn/img_convert/4ad3b539bee9bfe9a6acdba476ceed78.gif" alt="快速排序"></p>
<pre class=" language-java"><code class="language-java"><span class="token keyword">public</span> <span class="token keyword">static</span> <span class="token keyword">void</span> <span class="token function">quickSort</span><span class="token punctuation">(</span><span class="token keyword">int</span><span class="token punctuation">[</span><span class="token punctuation">]</span> arr<span class="token punctuation">,</span> <span class="token keyword">int</span> left<span class="token punctuation">,</span> <span class="token keyword">int</span> right<span class="token punctuation">)</span> <span class="token punctuation">{</span>

    <span class="token keyword">int</span> l <span class="token operator">=</span> left<span class="token punctuation">;</span> <span class="token comment" spellcheck="true">//左索引</span>
    <span class="token keyword">int</span> r <span class="token operator">=</span> right<span class="token punctuation">;</span> <span class="token comment" spellcheck="true">//右索引</span>

    <span class="token comment" spellcheck="true">// pivot 中轴</span>
    <span class="token keyword">int</span> pivot <span class="token operator">=</span> arr<span class="token punctuation">[</span><span class="token punctuation">(</span>left <span class="token operator">+</span> right<span class="token punctuation">)</span> <span class="token operator">/</span> <span class="token number">2</span><span class="token punctuation">]</span><span class="token punctuation">;</span>
    <span class="token keyword">int</span> temp <span class="token operator">=</span> <span class="token number">0</span><span class="token punctuation">;</span>
    <span class="token comment" spellcheck="true">//while循环的目的是让比pivot小的值放在他的左边</span>
    <span class="token comment" spellcheck="true">//pivot大的值放在他的右边</span>
    <span class="token keyword">while</span> <span class="token punctuation">(</span>l <span class="token operator">&lt;</span> r<span class="token punctuation">)</span> <span class="token punctuation">{</span>

        <span class="token keyword">while</span> <span class="token punctuation">(</span>arr<span class="token punctuation">[</span>l<span class="token punctuation">]</span> <span class="token operator">&lt;</span> pivot<span class="token punctuation">)</span> <span class="token punctuation">{</span>
            l <span class="token operator">+=</span> <span class="token number">1</span><span class="token punctuation">;</span>
        <span class="token punctuation">}</span>
        <span class="token keyword">while</span> <span class="token punctuation">(</span>arr<span class="token punctuation">[</span>r<span class="token punctuation">]</span> <span class="token operator">></span> pivot<span class="token punctuation">)</span> <span class="token punctuation">{</span>
            r <span class="token operator">-=</span> <span class="token number">1</span><span class="token punctuation">;</span>
        <span class="token punctuation">}</span>
        <span class="token comment" spellcheck="true">//说明pivot的左右两边的值已经按照左边全部是小于pivot，右边大于pivot</span>
        <span class="token keyword">if</span> <span class="token punctuation">(</span>l <span class="token operator">>=</span> r<span class="token punctuation">)</span> <span class="token punctuation">{</span>

            <span class="token keyword">break</span><span class="token punctuation">;</span>

        <span class="token punctuation">}</span>

        <span class="token comment" spellcheck="true">//交换</span>
        temp <span class="token operator">=</span> arr<span class="token punctuation">[</span>l<span class="token punctuation">]</span><span class="token punctuation">;</span>
        arr<span class="token punctuation">[</span>l<span class="token punctuation">]</span> <span class="token operator">=</span> arr<span class="token punctuation">[</span>r<span class="token punctuation">]</span><span class="token punctuation">;</span>
        arr<span class="token punctuation">[</span>r<span class="token punctuation">]</span> <span class="token operator">=</span> temp<span class="token punctuation">;</span>

        <span class="token comment" spellcheck="true">//如果交换玩后，发现这个arr[l] = pivot 相等 r-- ，前移一步</span>
        <span class="token keyword">if</span> <span class="token punctuation">(</span>arr<span class="token punctuation">[</span>l<span class="token punctuation">]</span> <span class="token operator">==</span> pivot<span class="token punctuation">)</span> <span class="token punctuation">{</span>
            r<span class="token operator">--</span><span class="token punctuation">;</span>
        <span class="token punctuation">}</span>

        <span class="token comment" spellcheck="true">//如果交换玩后，发现这个arr[r] = pivot 相等 l++ ，前移一步</span>
        <span class="token keyword">if</span> <span class="token punctuation">(</span>arr<span class="token punctuation">[</span>r<span class="token punctuation">]</span> <span class="token operator">==</span> pivot<span class="token punctuation">)</span> <span class="token punctuation">{</span>
            l<span class="token operator">++</span><span class="token punctuation">;</span>
        <span class="token punctuation">}</span>

    <span class="token punctuation">}</span>

    <span class="token comment" spellcheck="true">//如果l  == r,必须l++ ， r --，否则栈溢出</span>

    <span class="token keyword">if</span> <span class="token punctuation">(</span>l <span class="token operator">==</span> r<span class="token punctuation">)</span> <span class="token punctuation">{</span>
        l <span class="token operator">+=</span> <span class="token number">1</span><span class="token punctuation">;</span>
        r <span class="token operator">-=</span> <span class="token number">1</span><span class="token punctuation">;</span>
    <span class="token punctuation">}</span>
    <span class="token comment" spellcheck="true">//向左递归</span>
    <span class="token keyword">if</span> <span class="token punctuation">(</span>left <span class="token operator">&lt;</span> r<span class="token punctuation">)</span> <span class="token punctuation">{</span>
        <span class="token function">quickSort</span><span class="token punctuation">(</span>arr<span class="token punctuation">,</span> left<span class="token punctuation">,</span> r<span class="token punctuation">)</span><span class="token punctuation">;</span>
    <span class="token punctuation">}</span>
    <span class="token comment" spellcheck="true">//向右递归</span>
    <span class="token keyword">if</span> <span class="token punctuation">(</span>right <span class="token operator">></span> l<span class="token punctuation">)</span> <span class="token punctuation">{</span>
        <span class="token function">quickSort</span><span class="token punctuation">(</span>arr<span class="token punctuation">,</span> l<span class="token punctuation">,</span> right<span class="token punctuation">)</span><span class="token punctuation">;</span>
    <span class="token punctuation">}</span>


<span class="token punctuation">}</span>
</code></pre>
<h2 id="6-基数排序"><a href="#6-基数排序" class="headerlink" title="6.基数排序"></a>6.基数排序</h2><p><img src="https://upload-images.jianshu.io/upload_images/1940317-0fbcf53f27e12a87.gif?imageMogr2/auto-orient/strip%7CimageView2/2/w/959/format/webp" alt="img"></p>
<pre class=" language-java"><code class="language-java"><span class="token comment" spellcheck="true">//基数排序,又称桶排序</span>
<span class="token keyword">public</span> <span class="token keyword">static</span> <span class="token keyword">void</span> <span class="token function">radixSort</span><span class="token punctuation">(</span><span class="token keyword">int</span><span class="token punctuation">[</span><span class="token punctuation">]</span> arr<span class="token punctuation">)</span> <span class="token punctuation">{</span>

    <span class="token comment" spellcheck="true">//得到每个数组最大的数</span>
    <span class="token keyword">int</span> max <span class="token operator">=</span> arr<span class="token punctuation">[</span><span class="token number">0</span><span class="token punctuation">]</span><span class="token punctuation">;</span>  <span class="token comment" spellcheck="true">//假设第一个数据是最大的数</span>
    <span class="token keyword">for</span> <span class="token punctuation">(</span><span class="token keyword">int</span> i <span class="token operator">=</span> <span class="token number">0</span><span class="token punctuation">;</span> i <span class="token operator">&lt;</span> arr<span class="token punctuation">.</span>length<span class="token punctuation">;</span> i<span class="token operator">++</span><span class="token punctuation">)</span> <span class="token punctuation">{</span>

        <span class="token keyword">if</span> <span class="token punctuation">(</span>arr<span class="token punctuation">[</span>i<span class="token punctuation">]</span> <span class="token operator">></span> arr<span class="token punctuation">[</span><span class="token number">0</span><span class="token punctuation">]</span><span class="token punctuation">)</span> <span class="token punctuation">{</span>

            max <span class="token operator">=</span> arr<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token punctuation">;</span>
        <span class="token punctuation">}</span>


    <span class="token punctuation">}</span>

    <span class="token comment" spellcheck="true">//得到最大的数字几位数</span>
    <span class="token keyword">int</span> maxLength <span class="token operator">=</span> <span class="token punctuation">(</span>max <span class="token operator">+</span> <span class="token string">""</span><span class="token punctuation">)</span><span class="token punctuation">.</span><span class="token function">length</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">;</span>


    <span class="token comment" spellcheck="true">//第一轮（针对每个元素的个位数进行处理）</span>

    <span class="token comment" spellcheck="true">//定义一个二维数组，表示10个桶</span>

    <span class="token keyword">int</span><span class="token punctuation">[</span><span class="token punctuation">]</span><span class="token punctuation">[</span><span class="token punctuation">]</span> bucket <span class="token operator">=</span> <span class="token keyword">new</span> <span class="token class-name">int</span><span class="token punctuation">[</span><span class="token number">10</span><span class="token punctuation">]</span><span class="token punctuation">[</span>arr<span class="token punctuation">.</span>length<span class="token punctuation">]</span><span class="token punctuation">;</span>


    <span class="token comment" spellcheck="true">//为了记录每个桶中实际存放了多少个数据，我们定义一个一维数组来记录各个桶每次放入的数据个数</span>
    <span class="token keyword">int</span><span class="token punctuation">[</span><span class="token punctuation">]</span> bucketElementCounts <span class="token operator">=</span> <span class="token keyword">new</span> <span class="token class-name">int</span><span class="token punctuation">[</span><span class="token number">10</span><span class="token punctuation">]</span><span class="token punctuation">;</span>


    <span class="token comment" spellcheck="true">//这里使用循环处理maxLength</span>
    <span class="token keyword">for</span> <span class="token punctuation">(</span><span class="token keyword">int</span> i <span class="token operator">=</span> <span class="token number">0</span><span class="token punctuation">,</span> n <span class="token operator">=</span> <span class="token number">1</span><span class="token punctuation">;</span> i <span class="token operator">&lt;</span> maxLength<span class="token punctuation">;</span> i<span class="token operator">++</span><span class="token punctuation">,</span> n <span class="token operator">*=</span> <span class="token number">10</span><span class="token punctuation">)</span> <span class="token punctuation">{</span>
        <span class="token keyword">for</span> <span class="token punctuation">(</span><span class="token keyword">int</span> j <span class="token operator">=</span> <span class="token number">0</span><span class="token punctuation">;</span> j <span class="token operator">&lt;</span> arr<span class="token punctuation">.</span>length<span class="token punctuation">;</span> j<span class="token operator">++</span><span class="token punctuation">)</span> <span class="token punctuation">{</span>
            <span class="token comment" spellcheck="true">//取出每个元素的各位</span>
            <span class="token keyword">int</span> digitOfElement <span class="token operator">=</span> arr<span class="token punctuation">[</span>j<span class="token punctuation">]</span> <span class="token operator">/</span> n <span class="token operator">%</span> <span class="token number">10</span><span class="token punctuation">;</span>
            <span class="token comment" spellcheck="true">//放入到对应的桶中</span>
            bucket<span class="token punctuation">[</span>digitOfElement<span class="token punctuation">]</span><span class="token punctuation">[</span>bucketElementCounts<span class="token punctuation">[</span>digitOfElement<span class="token punctuation">]</span><span class="token punctuation">]</span> <span class="token operator">=</span> arr<span class="token punctuation">[</span>j<span class="token punctuation">]</span><span class="token punctuation">;</span>

            bucketElementCounts<span class="token punctuation">[</span>digitOfElement<span class="token punctuation">]</span><span class="token operator">++</span><span class="token punctuation">;</span>

        <span class="token punctuation">}</span>
        <span class="token comment" spellcheck="true">//按照这个桶的顺序取数据</span>
        <span class="token keyword">int</span> index <span class="token operator">=</span> <span class="token number">0</span><span class="token punctuation">;</span>

        <span class="token keyword">for</span> <span class="token punctuation">(</span><span class="token keyword">int</span> k <span class="token operator">=</span> <span class="token number">0</span><span class="token punctuation">;</span> k <span class="token operator">&lt;</span> <span class="token number">10</span><span class="token punctuation">;</span> k<span class="token operator">++</span><span class="token punctuation">)</span> <span class="token punctuation">{</span>
            <span class="token comment" spellcheck="true">//如果桶中有数据，我们才放回原数组</span>
            <span class="token keyword">if</span> <span class="token punctuation">(</span>bucketElementCounts<span class="token punctuation">[</span>k<span class="token punctuation">]</span> <span class="token operator">!=</span> <span class="token number">0</span><span class="token punctuation">)</span> <span class="token punctuation">{</span>
                <span class="token comment" spellcheck="true">//循环第k个桶，即第k个以为数组</span>
                <span class="token keyword">for</span> <span class="token punctuation">(</span><span class="token keyword">int</span> l <span class="token operator">=</span> <span class="token number">0</span><span class="token punctuation">;</span> l <span class="token operator">&lt;</span> bucketElementCounts<span class="token punctuation">[</span>k<span class="token punctuation">]</span><span class="token punctuation">;</span> l<span class="token operator">++</span><span class="token punctuation">)</span> <span class="token punctuation">{</span>
                    <span class="token comment" spellcheck="true">//取出元素放入到array中</span>
                    arr<span class="token punctuation">[</span>index<span class="token punctuation">]</span> <span class="token operator">=</span> bucket<span class="token punctuation">[</span>k<span class="token punctuation">]</span><span class="token punctuation">[</span>l<span class="token punctuation">]</span><span class="token punctuation">;</span>
                    index<span class="token operator">++</span><span class="token punctuation">;</span>
                <span class="token punctuation">}</span>
            <span class="token punctuation">}</span>
            <span class="token comment" spellcheck="true">//第一轮后，需要bucketElementCounts置0</span>

            bucketElementCounts<span class="token punctuation">[</span>k<span class="token punctuation">]</span> <span class="token operator">=</span> <span class="token number">0</span><span class="token punctuation">;</span>


        <span class="token punctuation">}</span>

    <span class="token punctuation">}</span>
<span class="token punctuation">}</span>
</code></pre>
<h2 id="7-归并排序"><a href="#7-归并排序" class="headerlink" title="7.归并排序"></a>7.归并排序</h2><p><img src="https://img-blog.csdn.net/20180809102227861?watermark/2/text/aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzQwNDcyMzI4/font/5a6L5L2T/fontsize/400/fill/I0JBQkFCMA==/dissolve/70" alt="这里写图片描述"></p>
<pre class=" language-java"><code class="language-java"><span class="token comment" spellcheck="true">/**
 *
 * @param arr   需要排序的原始数组
 * @param left   左边有序序列的初始索引
 * @param mid     中间索引
 * @param right   右边的索引
 * @param temp     中转数组
 */</span>
<span class="token keyword">public</span> <span class="token keyword">static</span> <span class="token keyword">void</span> <span class="token function">merge</span><span class="token punctuation">(</span><span class="token keyword">int</span><span class="token punctuation">[</span><span class="token punctuation">]</span> arr<span class="token punctuation">,</span> <span class="token keyword">int</span> left<span class="token punctuation">,</span> <span class="token keyword">int</span> mid<span class="token punctuation">,</span> <span class="token keyword">int</span> right<span class="token punctuation">,</span> <span class="token keyword">int</span><span class="token punctuation">[</span><span class="token punctuation">]</span> temp<span class="token punctuation">)</span> <span class="token punctuation">{</span>

    <span class="token keyword">int</span> i <span class="token operator">=</span> left<span class="token punctuation">;</span>   <span class="token comment" spellcheck="true">//初始化i，左边有序序列的初始索引</span>

    <span class="token keyword">int</span> j <span class="token operator">=</span> mid <span class="token operator">+</span> <span class="token number">1</span><span class="token punctuation">;</span>    <span class="token comment" spellcheck="true">//初始化j，右边有序序列的初始索引</span>

    <span class="token keyword">int</span> t <span class="token operator">=</span> <span class="token number">0</span><span class="token punctuation">;</span>  <span class="token comment" spellcheck="true">//指向temp数组的当前索引</span>

    <span class="token comment" spellcheck="true">//(-)</span>
    <span class="token comment" spellcheck="true">//先把左右两边的数据按规则填充到temp中</span>
    <span class="token comment" spellcheck="true">//知道左右两边的有序序列，有一边处理完毕</span>
    <span class="token keyword">while</span> <span class="token punctuation">(</span>i <span class="token operator">&lt;=</span> mid <span class="token operator">&amp;&amp;</span> j <span class="token operator">&lt;=</span> right<span class="token punctuation">)</span> <span class="token punctuation">{</span>
        <span class="token keyword">if</span> <span class="token punctuation">(</span>arr<span class="token punctuation">[</span>i<span class="token punctuation">]</span> <span class="token operator">&lt;=</span> arr<span class="token punctuation">[</span>j<span class="token punctuation">]</span><span class="token punctuation">)</span> <span class="token punctuation">{</span>
            temp<span class="token punctuation">[</span>t<span class="token punctuation">]</span> <span class="token operator">=</span> arr<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token punctuation">;</span>
            t<span class="token operator">++</span><span class="token punctuation">;</span>
            i<span class="token operator">++</span><span class="token punctuation">;</span>
        <span class="token punctuation">}</span> <span class="token keyword">else</span> <span class="token punctuation">{</span>
            temp<span class="token punctuation">[</span>t<span class="token punctuation">]</span> <span class="token operator">=</span> arr<span class="token punctuation">[</span>j<span class="token punctuation">]</span><span class="token punctuation">;</span>
            t<span class="token operator">++</span><span class="token punctuation">;</span>
            j<span class="token operator">++</span><span class="token punctuation">;</span>
        <span class="token punctuation">}</span>
    <span class="token punctuation">}</span>

    <span class="token comment" spellcheck="true">//(二)</span>
    <span class="token comment" spellcheck="true">// 把有剩余数据的一方的数据一次全部填充到temp去</span>
    <span class="token keyword">while</span> <span class="token punctuation">(</span>i <span class="token operator">&lt;=</span> mid<span class="token punctuation">)</span> <span class="token punctuation">{</span>   <span class="token comment" spellcheck="true">//说明左边的序列还有剩余元素</span>
        temp<span class="token punctuation">[</span>t<span class="token punctuation">]</span> <span class="token operator">=</span> arr<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token punctuation">;</span>
        t<span class="token operator">++</span><span class="token punctuation">;</span>
        i<span class="token operator">++</span><span class="token punctuation">;</span>

    <span class="token punctuation">}</span>

    <span class="token keyword">while</span> <span class="token punctuation">(</span>j <span class="token operator">&lt;=</span> right<span class="token punctuation">)</span> <span class="token punctuation">{</span>   <span class="token comment" spellcheck="true">//说明右边的序列还有剩余元素</span>
        temp<span class="token punctuation">[</span>t<span class="token punctuation">]</span> <span class="token operator">=</span> arr<span class="token punctuation">[</span>j<span class="token punctuation">]</span><span class="token punctuation">;</span>
        t<span class="token operator">++</span><span class="token punctuation">;</span>
        j<span class="token operator">++</span><span class="token punctuation">;</span>

    <span class="token punctuation">}</span>
    <span class="token comment" spellcheck="true">//(三)</span>
    <span class="token comment" spellcheck="true">//将temp数组的元素拷贝到Arrays</span>
    t <span class="token operator">=</span> <span class="token number">0</span><span class="token punctuation">;</span>
    <span class="token keyword">int</span> tempLeft <span class="token operator">=</span> left<span class="token punctuation">;</span>
    <span class="token keyword">while</span> <span class="token punctuation">(</span>tempLeft <span class="token operator">&lt;=</span> right<span class="token punctuation">)</span> <span class="token punctuation">{</span>
        arr<span class="token punctuation">[</span>tempLeft<span class="token punctuation">]</span> <span class="token operator">=</span> temp<span class="token punctuation">[</span>t<span class="token punctuation">]</span><span class="token punctuation">;</span>
        t<span class="token operator">++</span><span class="token punctuation">;</span>
        tempLeft<span class="token operator">++</span><span class="token punctuation">;</span>
    <span class="token punctuation">}</span>


<span class="token punctuation">}</span>
</code></pre>

                
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